I've successfully used this method on a number of firearms with surface rust specks, and it leaves the underlying bluing intact. It's "old school" and has been around for awhile.
First, I literally marinate the area in WD-40 overnight, or longer, until it has completely softened the rust speck where with a bit of "encouragement", will break down.
The encouragement is in the form of a real copper penny, not the newer clad stuff (minted before 1983). Use the leading edge to lightly scrape and "work" the softened rust off the surface. The 95% copper penny is hard enough to take the rust off, but soft enough to not scrape the bluing in the process.
You will get copper smears from the penny as it wears away, but those will easily clean of with any bore cleaner for copper deposits.
Then, I just put a coat of gun oil. Trying to touch up the spots with cold blue usually results in making the stuff you want to eliminate/hide, stand out even worse.